P(winning) `(x)/(12)`, P(Losing) `=(1)/(3)`. Find x.

Answer

To solve the problem, we need to find the value of \( x \) given the probabilities of winning and losing.

### Step-by-Step Solution:

1. **Understand the Given Probabilities**:
- Probability of winning: \( P(\text{winning}) = \frac{x}{12} \)
- Probability of losing: \( P(\text{losing}) = \frac{1}{3} \)

2. **Use the Fundamental Probability Rule**:
- The sum of the probabilities of all possible outcomes must equal 1. Therefore, we can write:
\[ P(\text{winning}) + P(\text{losing}) = 1 \]
- Substituting the given probabilities:
\[ \frac{x}{12} + \frac{1}{3} = 1 \]

3. **Find a Common Denominator**:
- The common denominator between 12 and 3 is 12. We can rewrite \( \frac{1}{3} \) with a denominator of 12:
\[ \frac{1}{3} = \frac{4}{12} \]
- Now, substitute this back into the equation:
\[ \frac{x}{12} + \frac{4}{12} = 1 \]

4. **Combine the Fractions**:
- Combine the fractions on the left side:
\[ \frac{x + 4}{12} = 1 \]

5. **Cross-Multiply to Solve for \( x \)**:
- Cross-multiply to eliminate the fraction:
\[ x + 4 = 12 \]

6. **Isolate \( x \)**:
- Subtract 4 from both sides:
\[ x = 12 - 4 \]
- Therefore:
\[ x = 8 \]

### Final Answer:
The value of \( x \) is \( 8 \).